Category:Examples of Inductive Sets

From ProofWiki
Jump to navigation Jump to search

This category contains examples of Inductive Set.

Let $S$ be a set of sets.

Then $S$ is inductive if and only if:

\((1)\)   $:$   $S$ contains the empty set:    \(\ds \quad \O \in S \)      
\((2)\)   $:$   $S$ is closed under the successor mapping:      \(\ds \forall x:\) \(\ds \paren {x \in S \implies x^+ \in S} \)      where $x^+$ is the successor of $x$
  That is, where $x^+ = x \cup \set x$

Pages in category "Examples of Inductive Sets"

The following 2 pages are in this category, out of 2 total.